The logic of G. W. Leibniz (1646-1716) is usually considered as a pivot between traditional syllogistic and modern algebra of sets. Many historiographers believe that although Leibniz intended “to produce a calculus wider than traditional logic [...] he never succeeded in producing a calculus which covered even the whole theory of the syllogism” (Kneale 1962, p. 337). As a matter of fact, however, Leibniz not only discovered a fully axiomatized algebra of concepts (provably equivalent to Boolean algebra of sets), but he also anticipated important principles of contemporary systems of set-theory, quantifier logic, and modal propositional calculi.

Description of the contents of the tutorial:
This tutorial aims at reconstructing the following main components of Leibniz’s logic:

1. The algebra of concepts, L1, which can be viewed as the »intensional« counterpart of the ordinary (»extensional«) algebra of sets;
2. The extension of L1 by means of »indefinite concepts« which function as (second order) quantifiers;
3. A genius mapping of L1 into an algebra of propositions which gives rise to a calculus of strict implication;
4. The syntax and semantics of alethic and deontic modal logic.